## Cross Country Croquet

Wacky Methow sports…

modern methow cabin

*All of the posts under the "Off The Deep End" category.*

Wacky Methow sports…

Every year the opening of Highway 20 through the North Cascades National Park heralds a phase transition in the population density of the Methow Valley. From our home in Seattle to Winthrop this is the difference between 247 miles and 202 miles. For beautiful pictures of this years plowing of the road, see the WSDOT’s flickr page. Since the opening of the pass brings business, and busyness, locales like to try to predict the date it will open. So when will it open this year?

Here is a plot of the day of the year the road opened, and snow depth at the Swamp Creek snotel station on 3/1 of that year:

I’ve also calculated a least squares fit and plotted value of this fit for the given snow depth. Using this fit, and the fact that on 3/1 of this year there was 73 inches of snow, I can therefore predict, with absolute certainty (ha!) that Highway 20 will open on day 132 of this year, or May 12. A very late opening.

On February 11, 2013, Benedictus PP. XVI, a.k.a. Pope Benedictus XVI, also once known as Joseph Aloisius Ratzinger, announced that effective February 28, 2013, he was stepping down as Roman Pontiff (not abdication, resignation or renuntiatio). Pope Benedictus XVI was the 265th (or maybe 266th? or maybe 267th?) Bishop of Rome, perhaps the nineth pope to resign, not counting conditional resignation (important if you think you might get caught by Nazis.) Now normally, the comings and goings of the College of Cardinals would not stir me to write a blog post, especially not a blog post written in advice column style (so often used to convey certitude in the face of overwhelming selection bias.) But, you see, I was once a pontiff. Indeed according to Google for one brief period in 2004, I was once the top search result for this word. (Take that Beattles!)

Which is all to say, I thought it might be a good time to offer some advice to Pope Benedictus XVI for his life after leaving the papacy.

**Tip 1** It’s time to get serious about how your identity shapes your ego. You were once the leader of one billion souls, God’s main man on the ground, infallible and all that, but now you’re going to be living a humble monk’s life in a Vatican monastery. No longer infallible. No longer the leader of a billion souls (tweeter to 1.5 million.) You may think that your ego is separated from your job, but in my own transition from pseudo professor blogger to software developer it was quite a shock to no longer be able to rely on the accumulated status symbols that my job title carried along with it. In my case this meant no longer being introduced at parties as a “theoretical physicist doing quantum stuff.” In your case, people aren’t going to be kissing your ring any more (oh yeah, and you’ll have to give the ring up too!) My advice? I’d go for some Zen koans: Joshu’s dog and Zuigan Calls His Own Master would be a good place to start.

**Tip 2** You’re not going to get to travel all around the world anymore. Tip: volunteer to pick up people from the airport! Or visit an air museum where they will let you sit in airplane seats. Bonus tip: I find the air museum seats a really good way to fall asleep as well (If you can’t empathize with this, I would suggest you try getting up for way too many 6am flights, and you too will learn to fall asleep on contact with the too tight armrests of airline seats.)

**Tip 3** It’s going to be tough to keep up with your past life’s passion. When you got into the flow during your papal years, I’m sure there was no one able to compete with you for your knowledge and understanding of how to guide your flock forward. But now you are going to have to dedicate your time to your own solitary monastic life. You may think that this transition will not be abrupt, that you can slowly ween yourself from the papacy, but in my experience you’re not going to have the time to, say, give advice to the next Pope. Which is not to say that you have to give up you mission: you will just to choose what battles you’d like to carry forward. For me, it was self study of shortest vector in a lattice problems. For you, well I’m sure there is a suitable equivalent.

**Tip 4** You’re going to miss all of the friends around the world. Hopefully, if you’re lucky, some of them will start blogs. For you I’d suggest adding Whispers in Loggia to your RSS feed.

**Tip 5 **People are still going to look to you for expertise in your past life, but the slow creeping pace of entropy will gradually strip you of your knowledge of the secrets to the universe, and you’ll have to tell them that you don’t know. You’re just going to have to live with the accumulated slippage of your brain from the most up to date theology of our day. You can try to keep up, of course, though I’m not sure of what the equivalent of the arXiv is, but you’re just going to have to live with a new world where you say “I don’t know.” I recommend testing those words out every morning: “I don’t know.” “Nescio.” “Nescio.” “Nescio.”

The end of an era, pope. There is life afterwards, beyond an event horizon. Enjoy the transition, just hope that the black hole firewall ideas are wrong.

** **

Quantum computers are fascinating devices. Our current understanding of these devices is that they can do something that classical computers cannot: they can factor numbers in polynomial time (thank you Peter Shor!) Interestingly, however, we can’t prove that these devices outperform classical computers on any class of problems. What this means is something very particularly: we can’t show that the model of a quantum Turing machine can solve problems more efficiently than the classical model of a Turing machine. Complexity theorists say that we can’t show that BPP does not equal BQP. Complexity theorists remind me of my son learning new letters. Sorry I can’t help it. S. T. O. P. spells….stop!

A dark secret (okay it’s not really secret, but this is a blog) of classical computing is that we (or rather, they, since I’m as much a complexity theorist as I am handsomely good looking) also can’t say a lot along the same lines about classical computers. The most famous example of this, currently (2012), is that classically we don’t know whether there are computations which take polynomial (in the size of the problem) space and **unlimited** time, but can’t be done with just a polynomial (in the size of the problem) limit in time. In jargon this is the fact that we don’t know whether P (or BPP) equals PSPACE. That’s a huge gap, because PSPACE includes nearly everything in the sun, including computers which use time machines. That’s right. Classical complexity theory has yet to show that computers that use frickin’ time machines aren’t more powerful than the laptop I’m typing this on.

A reasonable person, I would think, given this state of affairs, would admit that we just don’t know and try to figure out more about the model of quantum computation. Interesting, however, academia attracts an interesting class of hyper smart person who try to get places in life by being contrarian. That’s great when it leads to results, and often it does. Being skeptical is an important part of the scientific process. But when it doesn’t lead to results, which I think is the current state of arguments about quantum computers, it leads to senior professors acting very unprofessionally, and stifling a field. Quantum computing is in exactly this state of existence. I can count the number of jobs given to theorists in quantum computing over the last decade on my hands. It’s far greater than the number of senior folks I’ve talked to who are credulously skeptical of quantum computers and show know better (i.e. they’ve at least read the relevant papers.) The number who are skeptical but who haven’t actually read the papers? My registers don’t count that high.

For an example of this phenomenon, hop on over at to the awesome and widely read blog Godel’s Lost Letter and P=NP where one of the coauthors of the blog Ken Regan has a post describing some work on trying to understanding the limits of quantum computers. That’s great! But in this post, Ken, who is an associate professor, can’t help but in a dig at quantum computers along the lines of “we can’t prove that it can’t do anything”:

But there is no proof today—let me repeat, no proof—that quantum circuits in BQP are not easy to simulate classically

Because I like poking tigers, and am no longer beholden to the whims of an academic community that strongly rejects quantum computing, I posted a comment (okay I’d post this even when I was a psuedo-professor) which included the last line

Oh, and, p.s. there is also no proof that classical circuits can’t solve NP-complete problems efficiently, but for some reason I don’t see that in all of your posts on classical computers

to which Ken responded

As for “no proof”, Dick provided some thoughts which I merged into my intro; I pondered upgrading that line to add “…, nor even a convincing hardness argument”—but thought that better left-alone in the post

So you can see the kind of thoughts that go through many theoretical computer scientists which confronted with quantum computing. Instead of “lets figure this out” the response is “I want to remind you that we haven’t proved anything, even though we also haven’t proved the same thing about likely even more powerful models of computation.” If you don’t think this isn’t a case of bias in academia, then you’re reading a different novel than I am. And if you don’t think this has an impact on junior academics, please see the correlation evidence of past hiring in academia (Or if you don’t like that: do an experiment. Give the damn people the jobs to hang themselves by. Or at least don’t give them advice to avoid quantum computing because of your own biases, I’m looking at you, you know who you are. Pffst!)

Like I said, however, I think focusing on making actual progress in understanding quantum computers is the important path to take (and to the credit of Ken, who I’m picking on simply because he’s at the top of the temporal queue of a long line of guys who like to pontificate about the power of quantum computers without having any arguments that go beyond “I think…”, he has tried to answer this question. But not without throwing in a backhand that he seems to find utterly professionally appropriate.) And of course the previous two paragraphs are enough of the same ad slander’n reasoning, but exactly from my own completely biased perspective. But toward being *ahem* productive, I’m completely convinced that quantum computers offer significant, proven, reasons to be built. This is a controversial statement, because I know all complexity theorists will disagree with this point of view. So this is aimed at the group of people with minds open enough to think not about complexity classes, but about real world experiments (we might call them, physicists.). 😉

The argument is almost as old as quantum computing itself. These are the so called “black-box” query complexity results in quantum computing, albeit as seen through a physicist’s measuring device. What these models do is as follows. They consider a set of black box functions (say functions from n bits to 1 bit, so-called binary functions) and ask one to identify something about this set of black box functions. For example, the set of functions could be all binary functions that are either constant (on all inputs they output 0 or on all inputs they output 1) or balanced (on half of inputs they output 0 and on the other half they output 1). Then the problem would be to distinguish whether, if I give you a machine that implements one of these functions, whether the function is constant or whether it is balanced. Then one “measures” the effectiveness of an algorithm for solving this by the number of times that you have to use the black box in order to figure out which set the function belongs to.

So what is the state of query complexity differences between classical and quantum computers? It can be proven that there are black box problems that can be solved by quantum computers using a polynomial number of queries in the size of the problem, but that **require** an exponential number of queries classical. That’s right. There is a proven exponential separation. (For those who would like to argue that the comparison is not fair because a quantum device that computes a function implements a different physics than that which gives you a classical computation, I would only note that our world is quantum mechanical, and we can compare a quantum querying of the quantum device to a classical one. A classical query of this quantum device is exponentially less efficient.)

At this point you may then wonder why all of the fuss about quantum computers not being proven to be more powerful than classical computers. The answer is interesting and starts with the way we set up the problem. We were given a black box that computes a classical function. We can think about this literally as a machine that we can’t probe any deeper into how it actually works. In this respect it is a sort of a-physical device, one that isn’t connected to the normal context of what a computation is (as modeled by, say a parallel Turing machine.) Suppose that this were a real physical device, then you could take it apart and look at how it worked. This means that you could get more information about the computation being performed. And when you allow this, well, it is then not clear that you couldn’t solve the problems for which quantum computers offer speedups just as fast on a classical computer. Thus while we know that with respect to these black box problems, quantum computers are exponentially faster than their classical brethren, we can’t carry this over to statements about models of computation.

But take a step back. Suppose you are an experimental physicist and I give you a black box and ask you to figure out whether the box implements one or another sets of functions. Well then, if you use this experimental device without peering into its innards, then you really really want to use a quantum computer for your experiment. The difference between exponential graduate students and polynomial graduate students is most certainly something that will get your grant funded by the NSF. Because the universe is quantum mechanical, damnit, and if you want to perform experiments that more quickly reveal how that universe operates, you’ve got to query it quantum mechanically to be most efficient.

Okay, you may not be convinced. You may argue that at its heart you can’t ever have a box that one can’t take apart and probe its innards (can you?) Fine. So I’ll modify the game a bit. I’ll give you a quantum system that is the output of the standard way this device if queried in these computeres $sum_x |x> |f(x)>$. Now you either get to query this using only classical measurements on this device in the computational basis, or you get to use the full power of quantum computers, querying with a measurement you can build in your quantum laboratory. In that case, you can show that a quantum experimentalist will exponentially outperform characterizing this state, i.e. solving the given promise problem. Think about this as a game, a game in which you can win by being quantum mechanical exponentially faster than you could being classical.

Of course this won’t convince anyone, especially not classical theoretical computer scientists (who once were at the vanguard of a totally new field, but now find themselves defending their own legacy code.) Does it at least pass the test of trying to present evidence in either direction for the power of quantum computers? Not really, for those who refuse to believe that quantum theory isn’t actually the right theory of nature. But it does seem to tell us something is fundamentally very very different about the ability to use quantum theory in a setting where you’re trying to extract information about an unknown quantum system. And it’s proven. And it’s not a way of thinking that the old guys would like you to think 🙂

What is my voice? Lacking one, I choose pseudo-plagiary (the original, far more illuminating, can be found here):

The other one, the one called Dave Bacon, is the one things happen to. I walk through the halls of Google Seattle and stop for a moment, perhaps mechanically now, to look at the green glow of code from flat screens, and the blocks and arrows on the whiteboard; I know of Dave Bacon from his email and see his name on a list of (former) professors or in another person’s blog. I like Borges, mountains, omphaloskepsis, the taste of chiles and the prose of Pynchon; he shares these preferences, but in a vain way that turns them histrionic. It would be an exaggeration to say that ours is a hostile relationship; I live, let myself go on living, so that Dave Bacon may have contrived his theories, and these theories justifies me. It is no effort for me to confess that he has achieved some valid pages (or more accurately he had great co-authors), but those pages cannot save me, perhaps because what is good belongs to no one, not even to him, but rather to the science and to experiment. Besides, I am destined to perish, definitively, and only some bits of information about myself can survive in him. Little by little, I am giving over everything to him, though I am quite aware of his perverse custom of flipping certain important bits about himself.

Feynman knew that all things change; the electron exchanges a photon with another electron, scattering to a new state. I shall remain in Dave Bacon, not scattered to another person (if it is true that my evolution is unitary), but I recognize myself less in his papers than in many others or in the laborious strumming of a guitar. Years ago I tried to free myself from him and went from the foundations of quantum theory to games correcting quantum computing machines, but those games belong to Dave Bacon now, and I shall have to imagine other things. Thus my life is a flight and I lose everything and everything belongs to oblivion, or to him.

I do not know which of us has written this webpage.

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